2. Pew Research in 2018 polled a random sample of 1058 U.S. teens (ages $$ 13-17 $$ ) about Internet use, $$ 44.7 \% $$ reported that they were online "almost constantly"-a fact of great interest to advertisers. Complete parts a through c below. a) Explain the meaning of $$ \hat{p}=0.447 $$ in the context of this situation. Choose the correct answer below. A. The meaning of $$ \hat{p}=0.447 $$ is that $$ 44.7 \% $$ of the 1058 teens in the sample reported that they were online "almost constantly." This is the researchers' best estimate of p, the proportion of all U.S. teens who would say that. B. The meaning of $$ \hat{p}=0.447 $$ is that $$ 44.7 \% $$ of the 1058 teens in the sample reported that they were online "almost constantly." This is the researchers' best estimate of $$ \hat{p} $$, the proportion of the 1058 teens in the sample who said that. C. The meaning of $$ \hat{p}=0.447 $$ is that the researchers have $$ 95 \% $$ confidence that $$ 44.7 \% $$ of all U.S. teens would report that they were online "almost constantly." D. The meaning of $$ \hat{p}=0.447 $$ is that the researchers have $$ 95 \% $$ confidence that $$ 44.7 \% $$ of the 1058 teens in the sample reported that they were online "almost constantly."

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We need to determine the correct interpretation of $$ \hat{p}=0.447 $$ in the context of the survey conducted by Pew Research. The symbol $$ \hat{p} $$ represents the sample proportion of teens who reported being online "almost constantly."
- **Option A** states that $$ \hat{p}=0.447 $$ is the best estimate of $$ p $$, the proportion of all U.S. teens. This is a correct interpretation because $$ \hat{p} $$ is used to estimate the population proportion $$ p $$.
- **Option B** suggests that $$ \hat{p}=0.447 $$ is the best estimate of $$ \hat{p} $$ itself, which is circular and does not provide meaningful information.
- **Option C** implies a confidence level about the population proportion, but it does not directly explain what $$ \hat{p} $$ represents.
- **Option D** also discusses confidence but focuses on the sample rather than the population.

Based on this analysis, Option A is the most accurate interpretation of $$ \hat{p}=0.447 $$.
A. The meaning of $$ \hat{p}=0.447 $$ is that $$ 44.7 \% $$ of the 1058 teens in the sample reported that they were online "almost constantly." This is the researchers' best estimate of $$ p $$, the proportion of all U.S. teens who would say that.

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